Maternity Leave?

Just had a baby 3 days ago, did you guys use paid parental leave and short term disability concurrently?? My hospital policy offers up to 12 weeks paid parental leave. I've been approved for 6 weeks, I'm still pending for the other 6 weeks bonding time. I also have short term disability insurance in which they opened a request for me. I was told to just email them of my baby's birth certificate and then the case manager will do the rest. I don't know if this can go concurrently or it might affect my pay. I know paid parental leave I think pays for my usual pay rate and short term disability I can get up to 70% of pay after taxes. Any input is highly encouraged. Thank you!